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Series- related word problem

  1. Jul 29, 2007 #1
    1. The problem statement, all variables and given/known data

    Here is the word problem:

    A cup of coffee contains about 120 mg of caffeine, while the half life of the caffeine in an adult is about 3.5 hours.

    1.) Suppose you ingest a cup of coffee every 6 hours. Obtain an expression for the amount of caffeine , A sub n, remaining in your body just before you drink your nth cup of coffee. Determine limit of [A sub n] as n approaches infinite.

    2.) Suppose you require a minimum of 70mg of caffeine to enjoy its benefits. . What is the longest time you can wait between successive cups pf coffee? (in hrs and minutes.)






    2. Relevant equations

    I believe the only relevant equation for this problem would be taking the half life of caffeine every 3.5 hours

    First assuming that a person doesn't take any more caffeine after the first cup, we have the following amounts of caffeine every 3.5 hours:

    end of 3.5 hrs=60mg
    7hrs=30mg
    10.5hrs=15mg
    14hrs=7.5mg
    17.5hrs=3.75mg
    21hrs=1.875mg
    24.5hrs=0.9375mg
    28hrs=0.46875mg

    we see the amount of caffeine approaching zero, correct?


    now I am having trouble correlating the amount of caffeine remaining after 6 hours. After 7 hrs we see that 2 half lives have occured. So if I can find out how much remains after 6 hours, then add the additional cup a series can be created. This is where I need help. Anyone have any idea?



    3. The attempt at a solution

    see above
     
  2. jcsd
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